Journal of High Energy Physics

, 2019:217 | Cite as

Neutrino telescopes as QCD microscopes

  • Valerio Bertone
  • Rhorry GauldEmail author
  • Juan Rojo
Open Access
Regular Article - Theoretical Physics


We present state-of-the-art predictions for the ultra-high energy (UHE) neutrino-nucleus cross-sections in charged- and neutral-current scattering. The calculation is performed in the framework of collinear factorisation at NNLO, extended to include the resummation of small-x BFKL effects. Further improvements are made by accounting for the free-nucleon PDF constraints provided by D-meson data from LHCb and assessing the impact of nuclear corrections and heavy-quark mass effects, which are treated at NLO. The calculations presented here should play an important role in the interpretation of future data from neutrino telescopes such as IceCube and KM3NeT, and highlight the opportunities that astroparticle experiments offer to study the strong interactions.


Deep Inelastic Scattering (Phenomenology) 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    T.K. Gaisser, F. Halzen and T. Stanev, Particle astrophysics with high-energy neutrinos, Phys. Rept. 258 (1995) 173 [Erratum ibid. 271 (1996) 355] [hep-ph/9410384] [INSPIRE].
  2. [2]
    F. Halzen and S.R. Klein, IceCube: an instrument for neutrino astronomy, Rev. Sci. Instrum. 81 (2010) 081101 [arXiv:1007.1247] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    F. Halzen and D. Hooper, High-energy neutrino astronomy: the cosmic ray connection, Rept. Prog. Phys. 65 (2002) 1025 [astro-ph/0204527] [INSPIRE].
  4. [4]
    IceCube collaboration, Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert, Science 361 (2018) 147.Google Scholar
  5. [5]
    L.A. Anchordoqui et al., Cosmic neutrino pevatrons: a brand new pathway to astronomy, astrophysics and particle physics, JHEAp 1-2 (2014) 1 [arXiv:1312.6587] [INSPIRE].
  6. [6]
    A. Esmaili and P.D. Serpico, Are IceCube neutrinos unveiling PeV-scale decaying dark matter?, JCAP 11 (2013) 054 [arXiv:1308.1105] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    A. Esmaili, S.K. Kang and P.D. Serpico, IceCube events and decaying dark matter: hints and constraints, JCAP 12 (2014) 054 [arXiv:1410.5979] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    K. Murase, R. Laha, S. Ando and M. Ahlers, Testing the dark matter scenario for PeV neutrinos observed in IceCube, Phys. Rev. Lett. 115 (2015) 071301 [arXiv:1503.04663] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    P.S.B. Dev et al., Heavy right-handed neutrino dark matter and PeV neutrinos at IceCube, JCAP 08 (2016) 034 [arXiv:1606.04517] [INSPIRE].CrossRefGoogle Scholar
  10. [10]
    A. Bhattacharya, A. Esmaili, S. Palomares-Ruiz and I. Sarcevic, Probing decaying heavy dark matter with the 4-year IceCube HESE data, JCAP 07 (2017) 027 [arXiv:1706.05746] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    A. Esmaili and A.Yu. Smirnov, Probing Non-Standard Interaction of Neutrinos with IceCube and DeepCore, JHEP 06 (2013) 026 [arXiv:1304.1042] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    J. Salvado, O. Mena, S. Palomares-Ruiz and N. Rius, Non-standard interactions with high-energy atmospheric neutrinos at IceCube, JHEP 01 (2017) 141 [arXiv:1609.03450] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    R. Gandhi, C. Quigg, M.H. Reno and I. Sarcevic, Neutrino interactions at ultrahigh-energies, Phys. Rev. D 58 (1998) 093009 [hep-ph/9807264] [INSPIRE].
  14. [14]
    IceCube collaboration, Observation of high-energy astrophysical neutrinos in three years of IceCube data, Phys. Rev. Lett. 113 (2014) 101101 [arXiv:1405.5303] [INSPIRE].
  15. [15]
    IceCube collaboration, First year performance of the IceCube neutrino telescope, Astropart. Phys. 26 (2006) 155 [astro-ph/0604450] [INSPIRE].
  16. [16]
    KM3Net collaboration, Letter of intent for KM3NeT 2.0, J. Phys. G 43 (2016) 084001 [arXiv:1601.07459] [INSPIRE].
  17. [17]
    BAIKAL collaboration, The Baikal underwater neutrino telescope: design, performance and first results, Astropart. Phys. 7 (1997) 263 [INSPIRE].
  18. [18]
    GRAND collaboration, The giant radio array for neutrino detection, EPJ Web Conf. 135 (2017) 02001 [arXiv:1702.01395] [INSPIRE].
  19. [19]
    ANITA collaboration, Observational constraints on the ultra-high energy cosmic neutrino flux from the second flight of the ANITA experiment, Phys. Rev. D 82 (2010) 022004 [Erratum ibid. D 85 (2012) 049901] [arXiv:1003.2961] [INSPIRE].
  20. [20]
    J. Rojo et al., The PDF4LHC report on PDFs and LHC data: results from Run I and preparation for Run II, J. Phys. G 42 (2015) 103103 [arXiv:1507.00556] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    J. Gao, L. Harland-Lang and J. Rojo, The structure of the proton in the LHC precision era, Phys. Rept. 742 (2018) 1 [arXiv:1709.04922] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    R.S. Thorne, A variable-flavor number scheme for NNLO, Phys. Rev. D 73 (2006) 054019 [hep-ph/0601245] [INSPIRE].
  23. [23]
    S. Forte, E. Laenen, P. Nason and J. Rojo, Heavy quarks in deep-inelastic scattering, Nucl. Phys. B 834 (2010) 116 [arXiv:1001.2312] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  24. [24]
    S. Alekhin and S. Moch, Heavy-quark deep-inelastic scattering with a running mass, Phys. Lett. B 699 (2011) 345 [arXiv:1011.5790] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    M. Guzzi, P.M. Nadolsky, H.-L. Lai and C.P. Yuan, General-mass treatment for deep inelastic scattering at two-loop accuracy, Phys. Rev. D 86 (2012) 053005 [arXiv:1108.5112] [INSPIRE].ADSGoogle Scholar
  26. [26]
    V. Bertone, A. Glazov, A. Mitov, A. Papanastasiou and M. Ubiali, Heavy-flavor parton distributions without heavy-flavor matching prescriptions, JHEP 04 (2018) 046 [arXiv:1711.03355] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    G. Altarelli, R.D. Ball and S. Forte, An anomalous dimension for small x evolution, Nucl. Phys. B 674 (2003) 459 [hep-ph/0306156] [INSPIRE].
  28. [28]
    C.D. White and R.S. Thorne, A global fit to scattering data with NLL BFKL resummations, Phys. Rev. D 75 (2007) 034005 [hep-ph/0611204] [INSPIRE].
  29. [29]
    M. Ciafaloni, D. Colferai, G.P. Salam and A.M. Stasto, A matrix formulation for small-x singlet evolution, JHEP 08 (2007) 046 [arXiv:0707.1453] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    G. Altarelli, R.D. Ball and S. Forte, Small x resummation with quarks: deep-inelastic scattering, Nucl. Phys. B 799 (2008) 199 [arXiv:0802.0032] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    M. Bonvini, S. Marzani and T. Peraro, Small-x resummation from HELL, Eur. Phys. J. C 76 (2016) 597 [arXiv:1607.02153] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    M. Gluck, S. Kretzer and E. Reya, Dynamical QCD predictions for ultrahigh-energy neutrino cross-sections, Astropart. Phys. 11 (1999) 327 [astro-ph/9809273] [INSPIRE].
  33. [33]
    A. Cooper-Sarkar and S. Sarkar, Predictions for high energy neutrino cross-sections from the ZEUS global PDF fits, JHEP 01 (2008) 075 [arXiv:0710.5303] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    R. Gandhi, C. Quigg, M.H. Reno and I. Sarcevic, Ultrahigh-energy neutrino interactions, Astropart. Phys. 5 (1996) 81 [hep-ph/9512364] [INSPIRE].
  35. [35]
    A. Connolly, R.S. Thorne and D. Waters, Calculation of high energy neutrino-nucleon cross sections and uncertainties using the MSTW parton distribution functions and implications for future experiments, Phys. Rev. D 83 (2011) 113009 [arXiv:1102.0691] [INSPIRE].ADSGoogle Scholar
  36. [36]
    A. Cooper-Sarkar, P. Mertsch and S. Sarkar, The high energy neutrino cross-section in the Standard Model and its uncertainty, JHEP 08 (2011) 042 [arXiv:1106.3723] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  37. [37]
    C.-Y. Chen, P.S. Bhupal Dev and A. Soni, Standard model explanation of the ultrahigh energy neutrino events at IceCube, Phys. Rev. D 89 (2014) 033012 [arXiv:1309.1764] [INSPIRE].ADSGoogle Scholar
  38. [38]
    D.A. Dicus, S. Kretzer, W.W. Repko and C. Schmidt, Ultrahigh-energy neutrino nucleon cross-sections and perturbative unitarity, Phys. Lett. B 514 (2001) 103 [hep-ph/0103207] [INSPIRE].
  39. [39]
    R. Fiore et al., Asymptotic neutrino-nucleon cross section and saturation effects, Phys. Rev. D 73 (2006) 053012 [hep-ph/0512259] [INSPIRE].
  40. [40]
    J.L. Albacete, J.I. Illana and A. Soto-Ontoso, Neutrino-nucleon cross section at ultrahigh energy and its astrophysical implications, Phys. Rev. D 92 (2015) 014027 [arXiv:1505.06583] [INSPIRE].ADSGoogle Scholar
  41. [41]
    V.P. Goncalves and D.R. Gratieri, Investigating the effects of the QCD dynamics in the neutrino absorption by the Earth’s interior at ultrahigh energies, Phys. Rev. D 92 (2015) 113007 [arXiv:1510.03186] [INSPIRE].ADSGoogle Scholar
  42. [42]
    C.A. Argüelles, F. Halzen, L. Wille, M. Kroll and M.H. Reno, High-energy behavior of photon, neutrino and proton cross sections, Phys. Rev. D 92 (2015) 074040 [arXiv:1504.06639] [INSPIRE].ADSGoogle Scholar
  43. [43]
    M.M. Block, L. Durand, P. Ha and D.W. McKay, Implications of a Froissart bound saturation of γ * + p deep inelastic scattering. II. Ultrahigh energy neutrino interactions, Phys. Rev. D 88 (2013) 013003 [arXiv:1302.6127] [INSPIRE].
  44. [44]
    J. Jalilian-Marian, Enhancement and suppression of the neutrino nucleon total cross-section at ultrahigh-energies, Phys. Rev. D 68 (2003) 054005 [Erratum ibid. D 70 (2004) 079903] [hep-ph/0301238] [INSPIRE].
  45. [45]
    M. Bonvini, S. Marzani and C. Muselli, Towards parton distribution functions with small-x resummation: HELL 2.0, JHEP 12 (2017) 117 [arXiv:1708.07510] [INSPIRE].
  46. [46]
    R.D. Ball et al., Intrinsic charm in a matched general-mass scheme, Phys. Lett. B 754 (2016) 49 [arXiv:1510.00009] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  47. [47]
    R.D. Ball et al., Parton distributions with small-x resummation: evidence for BFKL dynamics in HERA data, Eur. Phys. J. C 78 (2018) 321 [arXiv:1710.05935] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    xFitter Developers’ Team collaboration, Impact of low-x resummation on QCD analysis of HERA data, Eur. Phys. J. C 78 (2018) 621 [arXiv:1802.00064] [INSPIRE].
  49. [49]
    F. Caola, S. Forte and J. Rojo, Deviations from NLO QCD evolution in inclusive HERA data, Phys. Lett. B 686 (2010) 127 [arXiv:0910.3143] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    F. Caola, S. Forte and J. Rojo, HERA data and DGLAP evolution: theory and phenomenology, Nucl. Phys. A 854 (2011) 32 [arXiv:1007.5405] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    LHCb collaboration, Measurements of prompt charm production cross-sections in pp collisions at \( \sqrt{s}=5 \) TeV, JHEP 06 (2017) 147 [arXiv:1610.02230] [INSPIRE].
  52. [52]
    LHCb collaboration, Measurements of prompt charm production cross-sections in pp collisions at \( \sqrt{s}=13 \) TeV, JHEP 03 (2016) 159 [Erratum ibid. 09 (2016) 013] [arXiv:1510.01707] [INSPIRE].
  53. [53]
    LHCb collaboration, Prompt charm production in pp collisions at \( \sqrt{s}=7 \) TeV, Nucl. Phys. B 871 (2013) 1 [arXiv:1302.2864] [INSPIRE].
  54. [54]
    R. Gauld and J. Rojo, Precision determination of the small-x gluon from charm production at LHCb, Phys. Rev. Lett. 118 (2017) 072001 [arXiv:1610.09373] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    PROSA collaboration, Impact of heavy-flavour production cross sections measured by the LHCb experiment on parton distribution functions at low x, Eur. Phys. J. C 75 (2015) 396 [arXiv:1503.04581] [INSPIRE].
  56. [56]
    R. Gauld, J. Rojo, L. Rottoli and J. Talbert, Charm production in the forward region: constraints on the small-x gluon and backgrounds for neutrino astronomy, JHEP 11 (2015) 009 [arXiv:1506.08025] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    M. Cacciari, M.L. Mangano and P. Nason, Gluon PDF constraints from the ratio of forward heavy-quark production at the LHC at \( \sqrt{s}=7 \) and 13 TeV, Eur. Phys. J. C 75 (2015) 610 [arXiv:1507.06197] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    R. Enberg, M.H. Reno and I. Sarcevic, Prompt neutrino fluxes from atmospheric charm, Phys. Rev. D 78 (2008) 043005 [arXiv:0806.0418] [INSPIRE].ADSGoogle Scholar
  59. [59]
    R. Gauld et al., The prompt atmospheric neutrino flux in the light of LHCb, JHEP 02 (2016) 130 [arXiv:1511.06346] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    PROSA collaboration, Prompt neutrino fluxes in the atmosphere with PROSA parton distribution functions, JHEP 05 (2017) 004 [arXiv:1611.03815] [INSPIRE].
  61. [61]
    G. Gelmini, P. Gondolo and G. Varieschi, Prompt atmospheric neutrinos and muons: NLO versus LO QCD predictions, Phys. Rev. D 61 (2000) 036005 [hep-ph/9904457] [INSPIRE].
  62. [62]
    A.D. Martin, M.G. Ryskin and A.M. Stasto, Prompt neutrinos from atmospheric cc and bb production and the gluon at very small x, Acta Phys. Polon. B 34 (2003) 3273 [hep-ph/0302140] [INSPIRE].
  63. [63]
    A. Bhattacharya et al., Perturbative charm production and the prompt atmospheric neutrino flux in light of RHIC and LHC, JHEP 06 (2015) 110 [arXiv:1502.01076] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    A. Bhattacharya et al., Prompt atmospheric neutrino fluxes: perturbative QCD models and nuclear effects, JHEP 11 (2016) 167 [arXiv:1607.00193] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    M. Benzke et al., Prompt neutrinos from atmospheric charm in the general-mass variable-flavor-number scheme, JHEP 12 (2017) 021 [arXiv:1705.10386] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    F. Halzen and L. Wille, Charm contribution to the atmospheric neutrino flux, Phys. Rev. D 94 (2016) 014014 [arXiv:1605.01409] [INSPIRE].ADSGoogle Scholar
  67. [67]
    M.V. Garzelli, S. Moch and G. Sigl, Lepton fluxes from atmospheric charm revisited, JHEP 10 (2015) 115 [arXiv:1507.01570] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    D. de Florian, R. Sassot, P. Zurita and M. Stratmann, Global analysis of nuclear parton distributions, Phys. Rev. D 85 (2012) 074028 [arXiv:1112.6324] [INSPIRE].ADSGoogle Scholar
  69. [69]
    K.J. Eskola, P. Paakkinen, H. Paukkunen and C.A. Salgado, EPPS16: nuclear parton distributions with LHC data, Eur. Phys. J. C 77 (2017) 163 [arXiv:1612.05741] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    K. Kovarik et al., nCTEQ15 — Global analysis of nuclear parton distributions with uncertainties in the CTEQ framework, Phys. Rev. D 93 (2016) 085037 [arXiv:1509.00792] [INSPIRE].ADSGoogle Scholar
  71. [71]
    H. Khanpour and S. Atashbar Tehrani, Global analysis of nuclear parton distribution functions and their uncertainties at next-to-next-to-leading order, Phys. Rev. D 93 (2016) 014026 [arXiv:1601.00939] [INSPIRE].ADSGoogle Scholar
  72. [72]
    IceCube collaboration, Measurement of the multi-TeV neutrino cross section with IceCube using Earth absorption, Nature 551 (2017) 596 [arXiv:1711.08119] [INSPIRE].
  73. [73]
    M. Bustamante and A. Connolly, Measurement of the energy-dependent neutrino-nucleon cross section above 10 TeV using IceCube showers, arXiv:1711.11043 [INSPIRE].
  74. [74]
    M. Bonvini, Small-x phenomenology at the LHC and beyond: HELL 3.0 and the case of the Higgs cross section, Eur. Phys. J. C 78 (2018) 834 [arXiv:1805.08785] [INSPIRE].
  75. [75]
    V. Bertone, S. Carrazza and J. Rojo, APFEL: A PDF Evolution Library with QED corrections, Comput. Phys. Commun. 185 (2014) 1647 [arXiv:1310.1394] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  76. [76]
    E.L. Berger et al., Charm-quark production in deep-inelastic neutrino scattering at next-to-next-to-leading order in QCD, Phys. Rev. Lett. 116 (2016) 212002 [arXiv:1601.05430] [INSPIRE].ADSCrossRefGoogle Scholar
  77. [77]
    J. Gao, Massive charged-current coefficient functions in deep-inelastic scattering at NNLO and impact on strange-quark distributions, JHEP 02 (2018) 026 [arXiv:1710.04258] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    R.D. Ball et al., Impact of heavy quark masses on parton distributions and LHC phenomenology, Nucl. Phys. B 849 (2011) 296 [arXiv:1101.1300] [INSPIRE].ADSCrossRefGoogle Scholar
  79. [79]
    T. Hahn, CUBA: a library for multidimensional numerical integration, Comput. Phys. Commun. 168 (2005) 78 [hep-ph/0404043] [INSPIRE].
  80. [80]
    J.A. Formaggio and G.P. Zeller, From eV to EeV: neutrino cross sections across energy scales, Rev. Mod. Phys. 84 (2012) 1307 [arXiv:1305.7513] [INSPIRE].ADSCrossRefGoogle Scholar
  81. [81]
    NNPDF collaboration, Unbiased determination of the proton structure function F (2)p with faithful uncertainty estimation, JHEP 03 (2005) 080 [hep-ph/0501067] [INSPIRE].
  82. [82]
    V. Barger, E. Basso, Y. Gao and W.-Y. Keung, Neutrino signals in IceCube from weak production of top and charm quarks, Phys. Rev. D 95 (2017) 093002 [arXiv:1611.00773] [INSPIRE].ADSGoogle Scholar
  83. [83]
    The xFitter Developers Team collaboration, Impact of the heavy quark matching scales in PDF fits, Eur. Phys. J. C 77 (2017) 837 [arXiv:1707.05343] [INSPIRE].
  84. [84]
    L. Frankfurt, V. Guzey and M. Strikman, Leading twist nuclear shadowing phenomena in hard processes with nuclei, Phys. Rept. 512 (2012) 255 [arXiv:1106.2091] [INSPIRE].ADSCrossRefGoogle Scholar
  85. [85]
    S. Dulat et al., New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev. D 93 (2016) 033006 [arXiv:1506.07443] [INSPIRE].ADSGoogle Scholar
  86. [86]
    R. Gauld, Forward D predictions for pPb collisions and sensitivity to cold nuclear matter effects, Phys. Rev. D 93 (2016) 014001 [arXiv:1508.07629] [INSPIRE].ADSGoogle Scholar
  87. [87]
    LHCb collaboration, Study of prompt D 0 meson production in pPb collisions at \( \sqrt{s_{\mathrm{N}}}=5 \) TeV, JHEP 10 (2017) 090 [arXiv:1707.02750] [INSPIRE].
  88. [88]
    A. Kusina, J.-P. Lansberg, I. Schienbein and H.-S. Shao, Gluon shadowing in heavy-flavor production at the LHC, Phys. Rev. Lett. 121 (2018) 052004 [arXiv:1712.07024] [INSPIRE].ADSCrossRefGoogle Scholar
  89. [89]
    D. Boer et al., Gluons and the quark sea at high energies: Distributions, polarization, tomography, arXiv:1108.1713 [INSPIRE].
  90. [90]
    LHeC Study Group collaboration, A Large Hadron Electron collider at CERN: report on the physics and design concepts for machine and detector, J. Phys. G 39 (2012) 075001 [arXiv:1206.2913] [INSPIRE].
  91. [91]
    NNPDF collaboration, Parton distributions from high-precision collider data, Eur. Phys. J. C 77 (2017) 663 [arXiv:1706.00428] [INSPIRE].
  92. [92]
    H1, ZEUS collaboration, Combination of measurements of inclusive deep inelastic e ± p scattering cross sections and QCD analysis of HERA data, Eur. Phys. J. C 75 (2015) 580 [arXiv:1506.06042] [INSPIRE].
  93. [93]
    A. Guffanti and J. Rojo, Top production at the LHC: the impact of PDF uncertainties and correlations, Nuovo Cim. C 033 (2010) 65 [arXiv:1008.4671] [INSPIRE].Google Scholar
  94. [94]
    M. Czakon, D. Heymes and A. Mitov, High-precision differential predictions for top-quark pairs at the LHC, Phys. Rev. Lett. 116 (2016) 082003 [arXiv:1511.00549] [INSPIRE].ADSCrossRefGoogle Scholar
  95. [95]
    R.D. Ball and R.K. Ellis, Heavy quark production at high-energy, JHEP 05 (2001) 053 [hep-ph/0101199] [INSPIRE].
  96. [96]
    NNPDF collaboration, Reweighting NNPDFs: the W lepton asymmetry, Nucl. Phys. B 849 (2011) 112 [Erratum ibid. B 854 (2012) 926] [arXiv:1012.0836] [INSPIRE].
  97. [97]
    R.D. Ball et al., Reweighting and unweighting of parton distributions and the LHC W lepton asymmetry data, Nucl. Phys. B 855 (2012) 608 [arXiv:1108.1758] [INSPIRE].ADSCrossRefGoogle Scholar
  98. [98]
    P. Nason, S. Dawson and R.K. Ellis, The total cross-section for the production of heavy quarks in hadronic collisions, Nucl. Phys. B 303 (1988) 607 [INSPIRE].ADSCrossRefGoogle Scholar
  99. [99]
    P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [hep-ph/0409146] [INSPIRE].
  100. [100]
    S. Frixione, P. Nason and C. Oleari, Matching NLO QCD computations with parton shower simulations: the POWHEG method, JHEP 11 (2007) 070 [arXiv:0709.2092] [INSPIRE].ADSCrossRefGoogle Scholar
  101. [101]
    S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP 06 (2010) 043 [arXiv:1002.2581] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  102. [102]
    S. Frixione, P. Nason and G. Ridolfi, A positive-weight next-to-leading-order Monte Carlo for heavy flavour hadroproduction, JHEP 09 (2007) 126 [arXiv:0707.3088] [INSPIRE].ADSCrossRefGoogle Scholar
  103. [103]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].
  104. [104]
    T. Sjöstrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
  105. [105]
    P. Skands, S. Carrazza and J. Rojo, Tuning PYTHIA 8.1: the Monash 2013 Tune, Eur. Phys. J. C 74 (2014) 3024 [arXiv:1404.5630] [INSPIRE].
  106. [106]
    I. Helenius and H. Paukkunen, Revisiting the D-meson hadroproduction in general-mass variable flavour number scheme, JHEP 05 (2018) 196 [arXiv:1804.03557] [INSPIRE].ADSCrossRefGoogle Scholar
  107. [107]
    H.L. Lai et al., Improved parton distributions from global analysis of recent deep inelastic scattering and inclusive jet data, Phys. Rev. D 55 (1997) 1280 [hep-ph/9606399] [INSPIRE].
  108. [108]
    A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Parton distributions for the LHC, Eur. Phys. J. C 63 (2009) 189 [arXiv:0901.0002] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  109. [109]
    H1, ZEUS collaboration, Proton structure from HERA to LHC, in the proceedings of the 40th International Symposium on Multiparticle Dynamics (ISMD 2010), September 21–25, Antwerp, Belgium (2010), arXiv:1012.1438 [INSPIRE].
  110. [110]
    A.C. Vincent, C.A. Argüelles and A. Kheirandish, High-energy neutrino attenuation in the Earth and its associated uncertainties, JCAP 11 (2017) 012 [arXiv:1706.09895] [INSPIRE].ADSCrossRefGoogle Scholar
  111. [111]
    A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].ADSCrossRefGoogle Scholar
  112. [112]
    A. Denner, Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortsch. Phys. 41 (1993) 307 [arXiv:0709.1075] [INSPIRE].ADSGoogle Scholar

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics and AstronomyVU UniversityAmsterdamThe Netherlands
  2. 2.Nikhef Theory GroupAmsterdamThe Netherlands
  3. 3.Institute for Theoretical PhysicsETHZürichSwitzerland

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